The paper deals with simple and composite hypotheses in statistical models with i.i.d. observations and with arbitrary families dominated by[sigma]-finite measures and parametrized by vector-valued variables. It introduces[phi]-divergence testing statistics as alternatives to the classical ones:...

The problems of estimating parameters of statistical models for categorical data, and testing hypotheses about these models are studied. Asymptotic properties of estimators minimizing [phi]-divergence between theoretical and empirical vectors of means are established. Asymptotic distributions of...

The paper presents asymptotic distributions of [phi]-disparity goodness-of-fit statistics in product multinomial models, under hypotheses and alternatives assuming sparse and nonsparse cell frequencies. The [phi]-disparity statistics include the power divergences of Read and Cressie...

The prediction of vectors of small area quantities based on a multivariate Fay-Herriot model is addressed. For this, an empirical best linear unbiased predictor (EBLUP) of the target vector is used, where the model parameters are estimated by two different methods based on moments. The mean...

In continuous parametrized models with i.i.d. observations we consider finite quantizations. We study asymptotic properties of the estimators minimizing disparity between the observed and expected frequencies in the quantization cells, and asymptotic properties of the goodness of fit tests...